Method, apparatus and communication unit

ABSTRACT

A method, an apparatus and a communication unit for generating precoding feedback information in a multiple frequency radio transmission system are disclosed. A rank for precoding matrices, wherein the rank is constant over the multiple frequencies, is selected and a plurality of precoding matrices having the selected rank are selected. A different precoding matrix is selected for each frequency subset of the multiple frequencies.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 15/862,974, filed Jan. 5, 2018, entitled “METHOD, APPARATUS ANDCOMMUNICATION UNIT,” which is a continuation of U.S. patent applicationSer. No. 15/196,894, filed Jun. 29, 2016, entitled “METHOD, APPARATUSAND COMMUNICATION UNIT,” now U.S. Pat. No. 9,900,077, issued Feb. 20,2018, which is a continuation of U.S. patent application Ser. No.14/717,648, filed May 20, 2015, entitled “METHOD, APPARATUS ANDCOMMUNICATION UNIT,” now U.S. Pat. No. 9,413,446, issued Aug. 9, 2016,which is a continuation of U.S. patent application Ser. No. 14/284,683,filed May 22, 2014, entitled “METHOD, APPARATUS AND COMMUNICATION UNIT,”now U.S. Pat. No. 9,065,719, issued Jun. 23, 2015, which is acontinuation of U.S. patent application Ser. No. 13/478,447, filed May23, 2012, entitled “METHOD, APPARATUS AND COMMUNICATION UNIT,” now U.S.Pat. No. 8,761,692, issued on Jun. 24, 2014, which is a continuation ofU.S. patent application Ser. No. 12/194,640, filed Aug. 20, 2008,entitled “METHOD, APPARATUS AND COMMUNICATION UNIT,” now U.S. Pat. No.8,204,453, issued Jun. 19, 2012. The entire disclosures of which arehereby incorporated by reference in their entireties for all purposes,except for those sections, if any, that are inconsistent with thisspecification.

FIELD

This invention relates to methods for generating feedback information inradio transmission systems, devices for generating feedback informationin radio transmission systems and communication units in radiotransmission systems.

BACKGROUND

Multiple-input multiple-output (MIMO) communication systems use multipledata streams. Precoding can be provided to manipulate multiple datastreams in MIMO communication systems by applying precoding matrices tothe data streams.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates a method according to one exemplaryembodiment.

FIG. 2 schematically illustrates a device 20 according to one exemplaryembodiment.

FIG. 3 schematically illustrates a device 30 according to one exemplaryembodiment.

FIG. 4 is a graph illustrating a pillar diagram.

DETAILED DESCRIPTION

The following embodiments of the invention are described with referenceto the drawings, wherein like reference numerals are generally utilizedto refer to like elements throughout, and wherein the various structuresare not necessarily drawn to scale. In the following description, forpurposes of explanation, numerous specific details are set forth inorder to provide a thorough understanding of one or more aspects ofembodiments of the invention. It may be evident, however, to one skilledin the art that one or more aspects of the embodiments of the inventionmay be practiced with a lesser degree of these specific details. Inother instances, known structures and devices are shown in block diagramform in order to facilitate describing one or more aspects of theembodiments of the invention. The following description is therefore notto be taken in a limiting sense, and the scope of the invention isdefined by the appended claims.

Methods and apparatuses as described herein may be utilized for radiotransmission systems, in particular Multiple Input Multiple Output(MIMO) systems operating in Orthogonal Frequency Division Multiplex(OFDM) mode in one embodiment. The apparatuses disclosed may be embodiedin baseband segments of devices used for reception of radio signals,such as mobile phones, handheld devices and/or mobile radio receivers orin mobile radio base stations, in particular radio transmitters. Thedescribed apparatuses may be employed to perform methods as disclosedherein, although those methods may be performed in any other way aswell, in particular outside baseband chips of mobile radio receiversand/or mobile phones.

A radio transmission link, in particular an OFDM communication link maybe operable with an amount of N subcarriers, with N being an integerequal to or greater than 1. Subcarriers of such radio transmissionsystems may comprise a single frequency each. They may also comprise aplurality of frequencies, for example adjoining frequencies in afrequency range or any arbitrary subset of frequencies. In oneembodiment, the number of frequencies included in a subcarrier may notbe limited to any number of frequencies. For transmission of radiosignals, such as OFDM radio signals, NT transmit antennas may be used,for example in transmission diversity mode, to transmit the signals inNS modulated data streams di, wherein i ranges from 1 to N. The radiosignals may be received by NR receive antennas. Using this transmissionmethod, up to NS=min(NT,NR) modulated data streams di may be transmittedsimultaneously, i.e. multiplexed in space.

In one embodiment, the data streams di may have been modulated in thetransmission device, for example a mobile radio base station, usingmodulation techniques commonly known to one in the art. The modulateddata streams di may be precoded using a precoding matrix Pi having NTlines and NS columns and then be transmitted using the NT transmitantennas. The precoding matrices Pi may have complex values. Inparticular, the precoding matrices Pi may be chosen to originate fromthe codebook C defined in the 3GPP-LTE standard. The codebook C containsprecoding matrices P which satisfy the transmit power constraint:

∥P∥ ² _(F) =P _(T).  (1)

The modulated and precoded data streams P_(i)d_(i) may then betransmitted over transmission channels having channel transmissioncharacteristics H_(i). The channel transmission characteristics H_(i)may be estimated in the transmitter and/or the receiver. According tothe channel transmission characteristics H_(i) the precoding matricesP_(i) may be selected adaptively. Additionally the modulated, precodedand channel-modulated data streams H_(i)P_(i)d_(i) may be distorted byadditive spatially white Gaussian noise n_(i). The Gaussian noise may inparticular be dependent on the signal-to-noise ratio of the transmitteddata streams. A receive signal y_(i) at N_(R) antennas on subcarrier imay be:

y _(i) =H _(i) P _(i) d _(i) +n _(i).  (2)

Precoding matrices P_(i) may be selected dependent on the channelcharacteristics H_(i). In particular, precoding matrices P_(i) may beselected such that the data capacity of a MIMO communication linkemployed by the transmitter is optimally used, i.e. the data rate F ofthe communication channel is as high as possible. The data rate F of aMIMO communication link may be expressed as

F(P _(i) ;H _(i))=log₂ det(I+H _(i) P _(i) P _(i) ^(H) H _(i) ^(H) σH_(n) ⁻²),  (3)

wherein the superscript H denotes the adjoint matrix, i.e. the Hermitiantranspose, of the associated matrix, and σ_(n) denotes the strength ofthe additive spatially white Gaussian noise n_(i). Other choices for thefunction F describing the data rate may be applicable as well and suchvariations are contemplated as falling within the scope of theinvention.

The data rate F may depend on the choice of precoding matrices P_(i) andthe channel transmission characteristics H_(i). Different optimizationtechniques may be utilized to maximize the data rate F. Depending on thereceiver used for reception of the receive signal, different techniquesmay be used to extract the data from the receive signal, for exampleserial interference cancellation (SIC) or minimizing the mean squareerror (MMSE). Therefore, the optimization of the data rate may betailored according to the type of receiver according to variousembodiments of the invention. In one embodiment, techniques whichminimize the mean square error may be performed by using a linear MIMOequalizer (MMSE equalizer) in the receiver. Assuming a MMSE equalizer inthe receiver, the data rate FM to be optimized may be expressed as

F _(M)(P _(i) ;H _(i))=Σ_(k=1) ^(N) ^(S) log₂(1+SINR_(i,k))=−_(k=1) ^(N)^(S) log₂(σ_(n) ²└(P _(i) ^(H) H _(i) ^(H) H _(i) P _(i)+σ_(n) ²I)⁻¹┘_(k,k)),  (4)

wherein I denotes the unit matrix and SINR_(i,k) thesignal-to-interference-and-noise ratio of the k-th data stream onsubcarrier i. The optimization therefore may aim to maximize thesignal-to-interference-and-noise ratio SINR_(i,k) after equalization(post-equalization SINR) in one embodiment.

In one embodiment, the precoding matrices P_(i) may be selected suchthat for each subcarrier a different precoding matrix P_(i) is chosen.Additionally, for each subcarrier the rank R_(i) of the associatedprecoding matrix P_(i) may be selected independently of the ranks of theremaining subcarriers. If the radio transmission system is operatingaccording to the LTE standard in one embodiment, the ranks R_(i) of theprecoding matrices P_(i) are all equal to R over the whole frequencyband, i.e. the rank R is selected to be constant for each of theprecoding matrices P_(i). If the rank R is selected to be constant, theprecoding matrices P_(i) may be selected from a subset of the entiretyof precoding matrices P_(i). In other words, the selection process forthe precoding matrices P_(i) is restricted to the pool of precodingmatrices having the desired rank R.

In one embodiment, selecting precoding matrices P_(i) may includesolving an optimization problem. For different ranks R_(i) over everysubcarrier the optimization problem may be set to

$\begin{matrix}{{\max\limits_{{\{{P_{i} \in C}\}}_{i = 1}^{N}}{\sum\limits_{i = 1}^{N}{F\left( {P_{i};H_{i}} \right)}}} = {\max\limits_{{\{ R_{i}\}}_{i = 1}^{N}}\; {\max\limits_{{\{{P_{i} \in C_{R_{i}}}\}}_{i = 1}^{N}}{\sum\limits_{i = 1}^{N}{{F\left( {P_{i};H_{i}} \right)}.}}}}} & (5)\end{matrix}$

For a constant rank R over every subcarrier the optimization problemsimplifies to

$\begin{matrix}{\max\limits_{R}\; {\max\limits_{{\{{P_{i} \in C_{R}}\}}_{i = 1}^{N}}{\sum\limits_{i = 1}^{N}{{F\left( {P_{i};H_{i}} \right)}.}}}} & (6)\end{matrix}$

With the optimization problem given in equation (6) for every possibleR, every possible combination of precoding matrices P_(i) with thecorresponding rank R has to be evaluated.

FIG. 1 shows a method according to one exemplary embodiment. First,estimates for the channel transmission characteristics H_(i) may begenerated at 100. The estimates for the channel transmissioncharacteristics H_(i) may be provided in one embodiment by meanscommonly known to ones skilled in the art. The generated estimates maybe used to select a wideband precoding matrix P of 102. In other words,a precoding matrix P may be selected such that the data rate over thewhole frequency band is maximized in one embodiment. In one embodiment,the precoding matrix P may be selected to optimize the expression

$\begin{matrix}{\max\limits_{P \in C}{\sum\limits_{i = 1}^{N}{{F\left( {P;H_{i}} \right)}.}}} & (7)\end{matrix}$

Solving this particular optimization problem may be performed by usingan approximation for the sum in equation (7):

Σ_(i=1) ^(N) F(P;H _(i))≈F _(C)(P ^(H) R _(Tx) P),  (8)

wherein R_(Tx) is the maximum likelihood estimate of the transmitcorrelation matrix and F_(C)(M) may, for example, be a cost functiondefined by

F _(C)(M)=log₂ det(I+Mσ _(n) ²).  (9)

Other definitions for the cost function may be used as well inalternative embodiments, depending on the type of receiver receiving thereceive signal. The particular cost function F_(C)(M) as described inthis embodiment may be considered for serial interference cancellation(SIC) or minimizing the mean square error (MMSE) in the receiver. R_(Tx)(the maximum likelihood estimate of the transmit correlation matrix) mayfurther be defined as

R _(Tx) =N ⁻¹Σ_(i=1) ^(N) H _(i) ^(H) H _(i) ≈E(H _(i) ^(H) H),  (10)

wherein E(X) is the arithmetical mean function of the value X, i.e. theexpectation value of the variable X. When selecting the widebandprecoding matrix P the optimization problem to be solved may thus be

$\begin{matrix}{\max\limits_{P \in C}{\log_{2}{{\det \left( {I + {P^{H}R_{Tx}P\; \sigma_{n}^{- 2}}} \right)}.}}} & (11)\end{matrix}$

The optimization problem given in Equation (10) may describe a systemwith a SIC receiver. For a linear MMSE receiver, the optimizationproblem may become

$\begin{matrix}{{\min\limits_{P \in C}{\sum\limits_{i = 1}^{N_{s}}{\log_{2}\left( \left( {I + {P^{H}R_{Tx}P\; \sigma_{n}^{- 2}}} \right)_{k,k}^{- 1} \right)}}},} & (12)\end{matrix}$

which may be transformed into a minimization problem of the geometricmean of minimum MSEs

$\begin{matrix}{\min\limits_{P \in C}{\prod\limits_{k = 1}^{N_{s}}\; {\left( \left( {I + {P^{H}R_{Tx}P\; \sigma_{n}^{- 2}}} \right)_{k,k}^{- 1} \right).}}} & (13)\end{matrix}$

When the wideband precoding matrix P has been selected at 102 of FIG. 1according to one of the optimization problems given in equations (7),(11), (12) or (13), the rank R of the wideband precoding matrix P may beselected at 104 in one embodiment as the optimized wideband rank R,which may be held constant over the whole frequency band, i.e. over allN subcarriers i. The rank R may alternatively be selected according tothe mean transmit correlation matrix R_(Tx) over all subcarriers i.Feedback information regarding the selected wideband precoding matrix Pmay be output to other components at 106 in the radio transmissionsystem, in particular a precoding matrix index (PMI). Additionally,feedback information regarding the selected rank R may be output toother components at 108 in the radio transmission system. Feedbackinformation regarding the precoding matrix index (PMI) of the selectedwideband precoding matrix P and/or the selected rank R may betransmitted to the radio transmitter transmitting the modulated datastreams di in one embodiment.

In another step, optimization problems similar to optimization problemsgiven in equations (7), (11), (12) and/or (13) may be solved for eachsubcarrier i. Precoding matrices P_(i) may be selected at 110 from asubset of precoding matrices P_(i) having the previously selected rank Raccording to the optimization problem

$\begin{matrix}{\max\limits_{{\{{P_{i} \in C_{R}}\}}_{i = 1}^{N}}{\sum\limits_{i = 1}^{N}{{F\left( {P_{i};H_{i}} \right)}.}}} & (14)\end{matrix}$

If the optimization problem is to be solved, when a linear MMSEequalizer is assumed in the receiver in one embodiment, the respectiveoptimization problem may be

$\begin{matrix}{\min\limits_{{\{{P_{i} \in C_{R}}\}}_{i = 1}^{N}}{\sum\limits_{i = 1}^{N_{s}}{{\log_{2}\left( \left( {I + {P_{i}^{H}R_{Tx}P_{i}\sigma_{n}^{- 2}}} \right)_{k,k}^{- 1} \right)}.}}} & (15)\end{matrix}$

Similarly to equation (13), the optimization problem of equation (15)may be transformed to

$\begin{matrix}{\min\limits_{{\{{P_{i} \in C_{R}}\}}_{i = 1}^{N}}{\prod\limits_{k = 1}^{N_{s}}\; {\left( \left( {I + {P^{H}R_{Tx}P\; \sigma_{n}^{- 2}}} \right)_{k,k}^{- 1} \right).}}} & (16)\end{matrix}$

In equations (14) to (16), the subset CR of precoding matrices P_(i)only contains precoding matrices P_(i) with the selected rank R. Theprecoding matrices P_(i) for each subcarrier i may be selected dependingon the mean transmit correlation matrix over the frequencies in theassociated subcarrier i. Feedback information on the plurality ofselected precoding matrices P_(i) may be output to other components ofthe radio transmission system at 112, in particular to the transmitter,i.e. the base station of the radio transmission system. Feedback on theplurality of selected precoding matrices P_(i) may include precodingmatrix indices (PMI) of at least one of the plurality of precodingmatrices P_(i).

In FIG. 2 an apparatus 20 according to one exemplary embodiment isshown. The apparatus 20 may be a precoding feedback informationgenerator configured to generate precoding feedback information in aradio transmission system such as a MIMO communication system operablein an OFDM mode. The apparatus 20 may include a wideband precodingmatrix selector 21 and a narrow band precoding matrix selector 1. Thewideband precoding matrix selector 21 may be fed with estimates of thechannel transmission characteristics H_(i) and may output a selectedwideband precoding matrix P having a selected rank R to the narrow bandprecoding matrix selector 1. The narrow band precoding matrix selector 1may be configured to output a plurality of narrow band precodingmatrices P_(i) for each subcarrier i of the radio transmission systemand to output feedback information on the plurality of narrow bandprecoding matrices P_(i) for each subcarrier i, in particular precodingmatrix indices (PMI). The apparatus 20 may be configured to perform amethod as illustrated in FIG. 1 in one embodiment.

In FIG. 3 an apparatus 30 according to one exemplary embodiment isshown. The apparatus 30 may be a precoding feedback informationgenerator configured to generate precoding feedback information in aradio transmission system such as a MIMO communication system operablein an OFDM mode. The apparatus 30 may include a precoding matrix rankselector 31 and a precoding matrix selector 1. The precoding matrix rankselector 31 may be fed with estimates of the channel transmissioncharacteristics H_(i) and may output a selected rank for a precodingmatrix P to the precoding matrix selector 1. The precoding matrixselector 1 may be configured to output a plurality of precoding matricesP_(i) having the selected rank R output by the precoding matrix rankselector 31 for each subcarrier i of the radio transmission system, andfurther configured to output feedback information on the plurality ofnarrow band precoding matrices P_(i) for each subcarrier i, such asprecoding matrix indices (PMI) in one embodiment. The apparatus 30 mayin particular be configured to perform a method as illustrated in FIG.1.

In FIG. 4 a graph illustrating a pillar diagram is shown. As an example,an LTE system with a 2×4 MIMO link having four transmit antennas and tworeceive antennas, i.e. N_(T)=4, N_(R)=2, and 1200 subcarriers divided insub-bands of 48 subcarriers each is contemplated. The precoding matriceshave been selected from the precoding codebook C with a minimum feedbackperiod of 1 ms.

Pillars 41 to 48 represent the amounts of real value operations inmillion instructions per second for different real value operations indifferent computational methods. Pillars 41 to 44 show the amounts ofreal value additions in different computational methods. Pillar 41represents the number of real value additions, when evaluating precodingmatrices P_(i) for each sub-band of subcarriers according to equation(4) using a linear MMSE equalizer without evaluating a widebandprecoding matrix P having a constant rank R before. The associatedoptimization problem to be solved is given in equation (6). Pillars 42and 43 each represent the number of real value additions when solving anoptimization problem as given in equation (15), where narrow bandprecoding matrices P_(i) are selected, wherein pillar 42 represents theworst assumable case and pillar 43 represents the best assumable case.Both pillar 42 and pillar 43 show a considerably lower number of realvalue additions than pillar 41, since for the optimization problem ofequation (15) a considerably lower amount of function evaluations isnecessary than for the optimization problem of equation (6). Pillar 44represents the number of real value additions when solving anoptimization problem as given in equation (13), where an optimizedwideband precoding matrix P over a whole frequency band is selected.

Pillars 45 to 48 represent respective numbers as pillars 41 to 44,respectively, for real value multiplications instead of real valueadditions. Again, the number of real value additions for pillar 45 ishigher than the number of real value additions for pillars 46 and 47.

In addition, while a particular feature or aspect of an embodiment ofthe invention may have been disclosed with respect to only one ofseveral implementations, such feature or aspect may be combined with oneor more other features or aspects of the other implementations as may bedesired and advantageous for any given or particular application.Furthermore, to the extent that the terms “include”, “have”, “with”, orother variants thereof are used in either the detailed description orthe claims, such terms are intended to be inclusive in a manner similarto the term “comprise”. The terms “coupled” and “connected”, along withderivatives may have been used. It should be understood that these termsmay have been used to indicate that two elements co-operate or interactwith each other regardless whether they are in direct physical orelectrical contact, or they are not in direct contact with each other.Furthermore, it should be understood that embodiments of the inventionmay be implemented in discrete circuits, partially integrated circuitsor fully integrated circuits or programming means. Also, the term“exemplary” is merely meant as an example, rather than the best oroptimal. It is also to be appreciated that features and/or elementsdepicted herein are illustrated with particular dimensions relative toone another for purposes of simplicity and ease of understanding, andthat actual dimensions may differ substantially from that illustratedherein.

1. One or more non-transitory, computer-readable media havinginstructions that, when executed, cause a first device to: generatefirst feedback information to provide an indication of a widebandprecoding matrix for a frequency band, the first feedback information tobe fed back to a second device; generate second feedback information toprovide an indication of a narrowband precoding matrix for a subset offrequencies of the frequency band, the second feedback information to befed back to the second device; and process a modulated data streamtransmitted by the second device, wherein the modulated data stream istransmitted based on the wideband precoding matrix or the narrowbandprecoding matrix.
 2. The one or more non-transitory, computer-readablemedia of claim 1, wherein the instructions, when executed, further causethe first device to: select a rank; and generate third feedbackinformation to provide an indication of the selected rank.
 3. The one ormore non-transitory, computer-readable media of claim 2, wherein therank is for the frequency band or for the subset of frequencies.
 4. Theone or more non-transitory, computer-readable media of claim 2, whereinthe instructions, when executed, further cause the first device toselect the narrowband precoding matrix for the rank.
 5. The one or morenon-transitory, computer-readable media of claim 1, wherein thenarrowband precoding matrix is a first narrowband precoding matrix, thesubset of frequencies is a first subset of frequencies, and theinstructions, when executed, further cause the first device to: select asecond narrowband precoding matrix for a second subset of frequencies ofthe frequency band; and generate third feedback information to providean indication of the second narrowband precoding matrix.
 6. The one ormore non-transitory, computer-readable media of claim 1, wherein thenarrowband precoding matrix is selected according to 3GPP-LTE standard.7. The one or more non-transitory, computer-readable media of claim 1,wherein the instructions, when executed, further cause the first deviceto: select the narrowband precoding matrix from a codebook.
 8. The oneor more non-transitory, computer-readable media of claim 1, wherein theindication of the wideband precoding matrix is to indicate a widebandindex associated with wideband precoding matrix; and the indication ofthe narrowband precoding matrix is to indicate a narrowband indexassociated with narrowband precoding matrix.
 9. An apparatus comprising:wideband precoding matrix selector circuitry to select a widebandprecoding matrix for a frequency band; narrowband precoding matrixselector circuitry to select a narrowband precoding matrix for a subsetof frequencies of the frequency band; transmit circuitry to causeindications of the wideband precoding matrix and the narrowbandprecoding matrix to be transmitted to another apparatus; and receivecircuitry process a modulated data stream transmitted by the device,wherein the modulated data stream is transmitted based on the widebandprecoding matrix or the sub-band precoding matrix.
 10. The apparatus ofclaim 9, further comprising: rank selector circuitry to select a rank,wherein the transmit circuitry is to cause an indication of the selectedrank to be transmitted to the other apparatus.
 11. The apparatus ofclaim 10, wherein the rank is for the frequency band or for the subsetof frequencies.
 12. The apparatus of claim 10, wherein the narrowbandprecoding matrix selector circuitry is to select the narrowbandprecoding matrix based on the rank.
 13. The apparatus of claim 10,wherein the narrowband precoding matrix is a first narrowband precodingmatrix, the subset of frequencies is a first subset of frequencies, andthe instructions, when executed, further cause the first device to:select a second narrowband precoding matrix for a second subset offrequencies of the frequency band; and generate third feedbackinformation to provide an indication of the second narrowband precodingmatrix.
 14. The apparatus of claim 9, wherein the narrowband precodingmatrix is selected according to 3GPP-LTE standard.
 15. The apparatus ofclaim 9, wherein the narrowband precoding matrix selector circuitry isto select the narrowband precoding matrix from a codebook.
 16. Theapparatus of claim 9, wherein the indication of the wideband precodingmatrix is to indicate a wideband index associated with widebandprecoding matrix; and the indication of the narrowband precoding matrixis to indicate a narrowband index associated with narrowband precodingmatrix.
 17. One or more non-transitory, computer-readable media havinginstructions that, when executed, cause a first device to: determine,based on channel estimates, a wideband precoding matrix for a frequencyband; determine a narrowband precoding matrix for a subset offrequencies of the frequency band; generate one or more transmissions totransmit indications of the wideband precoding matrix and the narrowbandprecoding matrix to a second device; and means for receiving a datastream transmitted based on the wideband precoding matrix or thenarrowband precoding matrix.
 18. The one or more non-transitory,computer-readable media of claim 17, wherein the instructions, whenexecuted, further cause the first device to: determine a transmissionrank that is a wideband rank or a narrowband rank, wherein the one ormore transmissions are further to transmit an indication of thetransmission rank.
 19. The one or more non-transitory, computer-readablemedia of claim 18, wherein the instructions are to determine thenarrowband precoding matrix based on the transmission rank.
 20. The oneor more non-transitory, computer-readable media of claim 17, wherein theindications are indications of the wideband index associated with thewideband precoding matrix and a narrowband index associated with thenarrowband precoding matrix.